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Mohammad Golshani
Mohammad Golshani
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removed deprecated tag 'topology'; replaced $FPP$ with FPP as FPP is text, not math (feel free to revert the substitution $FPP$ --> FPP if you wish; better yet, use *FPP* or ***FPP*** if you desire some formatting)
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Ricardo Andrade
Ricardo Andrade
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Recall that a topological space $X$ has the fixed point property fixed point property ($FPP$FPP), if any continuous function $f: X\to X$ has a fixed point.

Is the notion of $FPP$FPP for topological spaces an absolute notion, more? More precisely:

Question. Is it consistent that a topological space $X$ has the $FPP$FPP in $V$, but it does not have the $FPP$FPP in some (cardinal preserving) generic extension of $V$?

Recall that a topological space $X$ has the fixed point property ($FPP$), if any continuous function $f: X\to X$ has a fixed point.

Is the notion of $FPP$ for topological spaces an absolute notion, more precisely:

Question. Is it consistent that a topological space $X$ has the $FPP$ in $V$, but it does not have the $FPP$ in some (cardinal preserving) generic extension of $V$?

Recall that a topological space $X$ has the fixed point property (FPP) if any continuous function $f: X\to X$ has a fixed point.

Is the notion of FPP for topological spaces an absolute notion? More precisely:

Question. Is it consistent that a topological space $X$ has the FPP in $V$, but it does not have the FPP in some (cardinal preserving) generic extension of $V$?

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Mohammad Golshani
Mohammad Golshani
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Is the notion of fixed point property for topological spaces an absolute notion?

Recall that a topological space $X$ has the fixed point property ($FPP$), if any continuous function $f: X\to X$ has a fixed point.

Is the notion of $FPP$ for topological spaces an absolute notion, more precisely:

Question. Is it consistent that a topological space $X$ has the $FPP$ in $V$, but it does not have the $FPP$ in some (cardinal preserving) generic extension of $V$?